[meadsjn]

The problem here would be why did the Neanderthals die out, without competition or aggression, from Homo Sapiens?

Perhaps the increasing cold leading to the last glacial maximum (~18000 years ago) had some adverse effects on the population.

Just a guess.

[Lucius Cornelius Sulla]

‘Perhaps the increasing cold leading to the last glacial maximum (~18000 years ago) had some adverse effects on the population.’

Not likely, IMHO. Neanderthals had survived several glacial minimums over their history, and disappeared likely after the last glacial minimum.